The England international left Aston Villa to join Mark Hughes' Blues earlier in the week for £12 million, ending a long-running transfer saga dating back 12 months when the 28-year-old appeared set to sign for Liverpool.
That move failed to materialise, with Rafael Benitez's side failing to meet Villa's £18 million valuation of the former Brighton youngster.
NEWS: Manchester City bag Barry for £12 million
And Spurs boss Redknapp says both he and the Reds were interested in recruiting the anchorman during the close-season, only to be "blown out of the water" by the cash-rich Eastlands outfit.
"This week, I tried to sign Gareth Barry. I felt he would be a good addition for Spurs and I knew we had to make a decent offer for a top England player," he said in The Sun.
"Liverpool were also prepared to make a big offer. But we have both been blown out of the water by Manchester City.
"They offered a far bigger transfer fee and are giving the lad much bigger wages. We could not get near.
"It's certainly not Gareth's fault that he is being given such a massive contract."
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